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Navalny's wife Yulia said on his Twitter feed that he was arrested outside his home about a half-hour before Monday's demonstration was to begin.
Another protester Yevgeny, 19, said he was expelled from university after participating in a previous rally.
The mood was tense ahead of the rally as some groups of protesters vowed to go to the authorised location.
The protests kicked off shortly afterwards.
Tens of thousands are rallying across Russian Federation to protest corruption and government stagnation, with many chants and signs aimed at Putin.
Navalny scheduled the protests against what he says is a corrupt system of rule overseen by Russian President Vladimir Putin.
In March, thousands joined protests in nearly 100 cities across Russian Federation, angered by a report Navalny published accusing Prime Minister Dmitry Medvedev of corruption.
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Navalny, a Kremlin foe who is seeking to run for president next year, is looking to build on momentum picked up during nationwide protests in March, which drew unexpectedly large crowds and ended with more than 1,000 people detained in Moscow alone.
Rallies have been planned in 169 different locations for Russia Day, a national holiday, on Monday (12 June).
The Moscow city government had previously approved the protest to be held in a square just outside the center.
Photographs and videos posted on Twitter showed large numbers of police at Tverskaya Street in the capital, a main thoroughfare near the Kremlin.
Police have warned that they will take action if protesters break the law.
"Tverskaya is ready for Navalny", the newspaper Vedemosti tweeted, noting the sandbags and other fortifications in place for the reenactment.
The Moscow city government called the venue change a "provocation". "He asked me to tell you that the plans (for the protest) are unchanged".
Reuters reporters saw a heavy advance police presence on and around the avenue with bus loads of riot police parked nearby, side roads blocked, and airport-style metal detectors installed at pinch points. It remains unclear too whether the Kremlin will let Navalny run for the presidency.
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The 41-year-old's anti-corruption videos have needled the country's most powerful and drawn a new generation into politics. His report on alleged corruption connected to Prime Minister Dmitry Medvedev was the focus of the March protests.
That same realization motivated Sergei Boyko, the head of Navalny's Novosibirsk office, to put his IT career on hold and get into politics.
Mr Navalny earlier called on supporters to attend anti-corruption rallies across Russian Federation.
The Moscow protest is due to run from 1100 to 1400 GMT.
"I want changes", wrote Navalny in a blog post last week.
While the Kremlin has sought to characterize the opposition as a Westernized, urban and out-of-touch elite, protests occuring in far-flung parts of Siberia - where photos suggested a turnout of hundreds - could demonstrate significant support.
Also planning to protest Monday were Muscovites angry at the city's plan to relocate as many as 1.6 million residents of Soviet-era low-rise apartment buildings, a plan they believe amounts to a violation of their rights to own property and to choose where to live.
After Navalny's arrest was broadcast on social media networks, many protesters arrived in the city center not knowing what the next move would be without the main organizer there to lead the rally.
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